Jean Raimbault

Speedy deletion nomination of Colette Moeglin

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A tag has been placed on Colette Moeglin requesting that it be speedily deleted from Wikipedia. This has been done under section A7 of the criteria for speedy deletion, because the article appears to be about a person or group of people, but it does not credibly indicate how or why the subject is important or significant: that is, why an article about that subject should be included in an encyclopedia. Under the criteria for speedy deletion, such articles may be deleted at any time. Please read more about what is generally accepted as notable.

If you think this page should not be deleted for this reason, you may contest the nomination by visiting the page and clicking the button labelled "Contest this speedy deletion". This will give you the opportunity to explain why you believe the page should not be deleted. However, be aware that once a page is tagged for speedy deletion, it may be removed without delay. Please do not remove the speedy deletion tag from the page yourself, but do not hesitate to add information in line with Wikipedia's policies and guidelines. If the page is deleted, and you wish to retrieve the deleted material for future reference or improvement, then please contact the deleting administrator. Mayur ^{(talk•Email)} 11:59, 24 August 2016 (UTC)

I think that Colette Moeglin is probably notable in Wikipedia's sense (see also WP:Notability (academics)), but the page does not have the necessary references to show that. Rather than delete it, I have moved it to Draft:Colette Moeglin where you can work on it. Regards, JohnCD (talk) 17:34, 24 August 2016 (UTC)

Thanks for the attention to this article. I'll try to make it a bit thicker soon. jraimbau (talk) 17:37, 24 August 2016 (UTC)

Kazhdan's property (T)

I agree with your comment. How about you go for it and write these sections you propose. Thanks, Mhym (talk) 15:53, 31 July 2017 (UTC)

I might do that eventually. I put the comment because this is a big load of work if it is to be done correctly and I'm not sure whether I'll be able to do that soon. Cheers, jraimbau (talk) 18:01, 31 July 2017 (UTC)

Rollback granted

Hi Jean Raimbault. After reviewing your request for "rollbacker", I have temporarily enabled rollback on your account until 2018-07-01. Keep in mind these things when going to use rollback:

• Getting rollback is no more momentous than installing Twinkle.
• Rollback should be used to revert clear cases of vandalism only, and not good faith edits.
• Rollback should never be used to edit war.
• If abused, rollback rights can be revoked.
• Use common sense.

If you no longer want rollback, contact me and I'll remove it. Also, for some more information on how to use rollback, see Wikipedia:Administrators' guide/Rollback (even though you're not an admin). I'm sure you'll do great with rollback, but feel free to leave me a message on my talk page if you run into troubles or have any questions about appropriate/inappropriate use of rollback. Thank you for helping to reduce vandalism. Happy editing! Swarm ♠ 08:21, 21 May 2018 (UTC)

Note

Note that all curves are graphs of various functions and all functions have graphs, often curved. Your insistence on the word "object" is mathematical snobbery. — Preceding unsigned comment added by 31.53.53.217 (talk) 07:03, 5 July 2018 (UTC)

I'm not sure who the snob is supposed to be here. Yes, if you want to be sophisticated and unhelpful any mathematical notions can likely be sufficiently generalised to encompass any other one. It's still clearer to use a notion at their lower common level of use. Do you think most people would think of, say, the elliptic curve $y^{2}z=x^{3}+3xz^{2}+z^{3}$ in $\mathbb {P} (\mathbb {C} ^{3})$ as a function? Cheers. jraimbau (talk) 07:09, 5 July 2018 (UTC)

Translation surface

Hi, I am not an expert on differential geometry. But I wrote an article on the German Wikipedia on Schiebfläche and would like to translate it into English. My question: What should this article to be named ? The natural translation would be "translation surface" which exists already.--Ag2gaeh (talk) 18:01, 18 November 2018 (UTC)

Hello @Ag2gaeh:. This seems to be a bit of a niche notion (of which I was not previously aware), and I don't know a name for that ("translation surface" refers to something completely different, as noted in your german article. The book by Glaeser that you cite has been translated to English (see https://mathscinet.ams.org/mathscinet-getitem?mr=3524980) but I could not find a copy. I would suggest that you ask this question on the WikiProject Mathematics talk page.

Some remarks:

• your "Schiebflächen" seem to be a generalisation of surfaces of revolution which are much more familiar to differential geometers; also ruled surfaces are somewhat similar to it;
• in computer graphics the notion of "lofted surface" (see eg. Freeform surface modelling, and this paper has more details) seems to be a generalisation of this notion but it's not obvious to see as the language used there is completely different from that used by mathematicians

Hope this is helpful. jraimbau (talk) 14:22, 19 November 2018 (UTC)

Linear algebraic groups

Hey, do you have a reference for the Lie–Kolchin theorem reference? Upon looking at the page, it's not obvious why your statement about conjugation of solvable subgroups are a corollary.

Also, I noticed you want to bring wikipedia up to date by making geometric group theory an accessible topic covered. Do you have a list of subjects contained within algebraic geometry which I can help add? I'm not super fluent with linear algebraic groups, but would be more than happy to help, especially with articles intersecting DAG, homotopy theory, and algebraic geometry. I know the Mixed Hodge module page could be improved, but I need to get a better handle of some of the group/representation theory before diving in. It seems like HTT's book (https://link.springer.com/book/10.1007/978-0-8176-4523-6) on D-modules, perverse sheaves, etc paves the way, but maybe you have any alternative ideas? Otherwise, could you answer specific technical questions/provide references? I would really like to get the main points from that point onto wikipedia, especially with lot's of examples. Wundzer (talk) 19:04, 30 September 2020 (UTC)

Regarding Lie's theorem implying that every (connected, I forgot to mention this hypothesis) solvable subgroup can be conjugated into the uppper triangular subgroup: this is a recurrence argument, written in the section "triangularisation" in the article (pick an eigenvector, then apply the theorem on some complementary subspace).

Regarding geometric group theory and algebraic geometry : in my (certainly non-exhaustive) experience the intersection lies in the theory of arithmetic groups where stuff like strong approximation and Bruhat--Tits buildings plays an important role. The necessary theory is kind of old and I have no idea whether more recent developments in algebraic geometry apply to this area (and I am very much unfamiliar with algebraic geometry past the basic stuff). I'll have a look at the book you mention. jraimbau (talk) 06:10, 1 October 2020 (UTC)

Do you know of any references for computing the automorphism group of a Lie algebra? How does this decompose with respect to the decomposition into semi-simple Lie algebras? What is the automorphism group of ${\mathfrak {so}}(3)$ for example? Is it $Spin(3)$ or $SO(3)$? Wundzer (talk) 17:18, 5 October 2020 (UTC)

In this case I think it should be the adjoint form, $\mathrm {PO} (3)$. In general the automorphism group should be the semidirect product of inner automorphisms (so the adjoint group) by the automorphisms of the Dynkin diagram which corresponds to outer automorphisms (there are none for type A1 so for ${\mathfrak {so}}(3)$ we get only $\mathrm {PO} (3)$). I'll try to check that as soon as possible and find a proper reference. jraimbau (talk) 16:26, 6 October 2020 (UTC)

Awesome, thanks! Wundzer (talk) 16:49, 7 October 2020 (UTC)

Merci bien!

Pour votre réponse à ma question vis-à-vis quasi-isometries. 2601:200:C000:1A0:395D:10FC:99B6:B1CD (talk) 04:28, 8 September 2021 (UTC)

I removed 56 from the "smooth true list" in Generalized Poincaré conjecture

Hello. I might be wrong, but I assumed the fact that sequence A001676 ( https://oeis.org/A001676/list ) in OEIS has a value of 2 (not 1) for n = 56 means that there is an exotic sphere (just one) in that dimension, which means the smooth Poincaré conjecture is false in that dimention. It occurred to me that there could be chiral mirror-images, as there's a note on the sequence connecting mentioning that it's the number of oriented diffeomorphism classes of differentiable structures, but I would assume that the non-exotic form (like one formed by taking the set of all points in R⁵⁷ that are the same distance (some positive real number) from a certain point) would be achiral. Of course, it could be that that OEIS sequence is wrong. If you decide to revert my edit, I'd appreciate it if you could explain what I got wrong in my analysis. Thanks. Kevin Lamoreau (talk) 02:10, 8 September 2022 (UTC)

Hello @Kevin Lamoreau:, thanks for notifying me. I believe that it is the oeis that is wrong in this instance. In the paper used as reference (https://arxiv.org/pdf/1601.02184.pdf, published in Annals) they state that until recently it was believed that $\mathbb {S} ^{56}$ had a nontrivial smooth structure but that an error was found recently in the computation for the obstruction and in fact this is not the case: see Theorem 1.14 there and the discussion before its statement. The preprint the authors refer to for this new computation has been published in 2019 (see https://zbmath.org/?q=an%3A1454.55001). If that is OK with you i will revert the edit to the previous version, and maybe add a note to mention the error. (I'm sorry to rely on papers and not be able to explain this properly but i'm not familiar in any depth with this area of topology; on the other hand the statements in the paper by Wang and Xu are very clear regarding this problem).

Regarding chirality i agree with you, the sphere in any dimension always has an orientation-reversing self-diffeomorphism. Cheers, jraimbau (talk) 06:37, 8 September 2022 (UTC)

Thanks for that information, @Jean Raimbault:. I've reverted my edit (so I've added the dimension 56 back to the "smooth true list"). I thought about putting a note in the section Order of Θ_n of the exotic sphere article about sequence A001676 being wrong for n = 56, but it sounds like it may be wrong for dimension 57 as well. Also, since the "number of oriented diffeomorphism classes" (with the possible exception of dimension 4) was not the definition of that sequence but a note, it could be (I don't know) that the value of 2 in the sequence (the number of h-cobordism classes of smooth homotopy 61-spheres) is correct, but that in that instance it doesn't coincide with the number of diffeomorphism classes. Hopefully someone more mathematically with it than I will correct whatever needs to be corrected with that sequence soon. Kevin Lamoreau (talk) 01:43, 9 September 2022 (UTC)

Thanks! jraimbau (talk) 05:31, 9 September 2022 (UTC)

Law of large numbers

That this only holds in the limit of $n\to \infty$ is expressed by "with a sufficiently large sample". Therefore, I removed "with very high probability". The equation says, this probability is 1.

For the strong law in the next paragraph of the article, the wording is similar: "What this means is that the probability that, as the number of trials n goes to infinity, the average of the observations converges to the expected value, is equal to one." Unless there is a difference I am missing, before my edit, the first sentence was redundant. --85 ^[?!] 18:18, 12 October 2022 (UTC)

Thank you for your message @Fuenfundachtzig:. Your statement is not correct. The formal statement of the weak law is that :

For any $\epsilon >0$ there exists $n_{0}$ such that for all $n\geq n_{0}$ the probability that $|S_{n}-\mu |<\epsilon$ is at least $1-\epsilon$.

(here $S_{n}$ is the average over $n$ trials and $\mu$ is the expected result of the experiment). In the informal version, "sufficiently large sample" refers to $n\geq n_{0}$; "with high probability" refers to $\mathbb {P} (|S_{n}-\mu |<\epsilon )>1-\epsilon$. Thus both statements are necessary to give a precise informal statement of the weak law.

Similarly, the strong law refers to the probability on the set of all infinite samples, but it does not say anything deterministic about any particular set of finite samples. jraimbau (talk) 06:58, 13 October 2022 (UTC)

Thanks for the explanation! Indeed, I missed that the limit is once inside and once outside the brackets. --85 ^[?!] 09:54, 28 October 2022 (UTC)

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Ergodicity

Hi! You've reverted edits to the article on ergodicity twice. Please do not do so a third time! If you do not understand a topic, section blanking is the inappropriate response. There are multiple alternatives: you can ask on the talk page (which you did, but did not indicate what parts were hard to understand). You can also approach me directly, on my talk page. If you find the entire topic difficult to understand, there are several on-line resources which can help you get answers. One of the finest is the mathematics stack exchange. I am now going to revert your revert, and hope that you can describe what you find confusing on the article talk page. I am quite willing to fix problems and clarify confusing text, and make this article easy to understand. (I cannot offer tutorial services.) 67.198.37.16 (talk) 14:17, 20 April 2023 (UTC)

Not going to answer these insults. Please don't edit this talk page again. jraimbau (talk) 07:23, 21 April 2023 (UTC)

Proposal: split ergodicity into two!?

I added the following proposal to the talk page; perhaps you might like it?

Copy or move the bottom half of the ergodicity article to a new article ergodicity (mathematics) that would then be free to accumulate formal definitions? Thus, ergodicity would contain the sketchy, informal introduction, while the new article would contain not only formal definitions, but would be of the right format to grow over time with formal results and theorems. 67.198.37.16 (talk) 15:19, 29 April 2023 (UTC)

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References for the Frobenius-Perron operator?

Hi, Sorry to bother you; you've clearly gone through one or two books on ergodic theory and/or measure-preserving dynamical systems. Do you recall if any of them give a reasonable/adequate treatment of the spectrum of the Frobenius-Perron operator? I learned the theory through a patchwork of papers; enough decades have passed that I figure someone must have collected up all of the assorted theorems and results from assorted published papers, and shaped them into some textbook. Are you aware of any? 67.198.37.16 (talk) 02:03, 25 November 2023 (UTC)

I'm not, sorry. I think in general not much can be said about the spectrum. The spectrum of Markov and Hecke operators, which are very similar to these though in different context, has been studied a lot. jraimbau (talk) 21:19, 25 November 2023 (UTC)

Thank you! 67.198.37.16 (talk) 21:31, 25 November 2023 (UTC)

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"Its" central series?

Hi – in this edit you replaced "a group that has a central series of finite length" by "its central series is of finite length". As far as I'm aware, there's no such thing as "its central series" – a group has a lower central series and an upper central series, but it can have any number of central series. I just wanted to check whether I'm missing something before I change it back. Joriki (talk) 09:45, 13 January 2024 (UTC)

It is equivalent for the ascending and descending central series to be of finite length so i don't think there is any ambiguity in this formulation. I also can't remember why i made this edit, i can't say i find any version better than the other so feel free to revert! if i have time i'll try to make it clearer at some point. Cheers, jraimbau (talk) 19:04, 13 January 2024 (UTC)

Thanks for the reply! I reverted because the definition later in the article also lists those three equivalent definitions, and it says "has a central series of finite length", referring not just to the upper and lower central series, but more generally to any central series. Joriki (talk) 18:35, 18 January 2024 (UTC)

Stop distorting sources

I have recently noticed your edits on the L.E.J. Brouwer article and I'm wondering why you're twisting the words on what the sources are actually saying. GoneWithThePuffery (talk) 02:52, 17 March 2024 (UTC)

could you substantiate that please? i don't want to start a conversation on a vague accusation. jraimbau (talk) 12:34, 17 March 2024 (UTC)

Vague accusation? I'm sorry but if you, for example, change the lead from "he is known as the founder of modern topology" to "he is one of the founders of modern topology", then you're purposefully distorting what the references actually say. We read in L.E.J. Brouwer's entry in the Stanford Encyclopedia: "In classical mathematics, he founded modern topology by establishing, for example, the topological invariance of dimension and the fixpoint theorem." We can read similar claims elsewhere. Why are you doing this? The same goes for the statement that Brouwer was one of the greatest mathematicians of the 20th century. You are contradicting everything that is backed by sources and you're making up your own story; that's WP:OWN RESEARCH, for the record. GoneWithThePuffery (talk) 13:00, 17 March 2024 (UTC)

Thank you for clarifying. I vever said the sources do not claim that, i said that the two i removed are not relevant. To wit :

• an article in an online art review cannot be seriously used to support a claim on the history of mathematics ;
• the second source seems more serious---i could not look at it as there is no link and i don't own the book---but given the stature of the claim (identifying "the founder" of an entire field of modern mathematics) a book seemingly about an entirely different subject than the history of topology cannot be used to support it by itself.

The SEoP entry certainly is useful as a source of bibli- and biographical facts on Brouwer but similarly it should not be used to support a claim about the history of mathematics.

For the record i note that neither the article on Poincaré nor that on Hilbert (both unarguably having had much greater influence on mathematics than Brouwer) contain an allusion to them being greatest in the lede, and i don't think such bolsterous language belongs in a serious mathematical article (as opposed to, say, sports). jraimbau (talk) 13:21, 17 March 2024 (UTC)

What are you talking about? You completely rewrote the sentence into something that doesn't add up with what the source says! Why did you do that?

An article in an online art review? I'm talking about The Stanford Encyclopedia and a book by Donald Gillies, a historian of science and mathematics published by Routledge. If that's not reliable then what is?

And by the way, by far not only the SEoP claims this, there are plenty of sources who state precisely the same.

Last but not least. How do you measure this influence when talking about Hilbert & Poincaré? Gillies talks about Hilbert and Brouwer in the same breath ("Two of the greatest mathematicians of the 20th century"). It could refer to importance, which in part has to do with influence, but not entirely. The article by Hilbert says: "one of the most influential mathematicians of the 19th and early 20th centuries", which comes pretty close to what the article on Brouwer now claims. The article by Grothendieck (to take someone else) says: "He is considered by many to be the greatest mathematician of the twentieth century." These claims are widespread on Wikipedia. Now, personally I don't agree with it as well, but on the other hand, if some articles make these kind of claims and others don't, then that's saying something as a matter of comparison. And also, for people who are not aware of certain people it might definitely be helpful. GoneWithThePuffery (talk) 23:36, 17 March 2024 (UTC)

I explained my changes in my edit sumaries and i gave precise arguments above to justify them. I stand by my claim that the sources are not adequate to support the claim that Brouwer is "the founder of modern topology" (otoh. i believe his results speak by themselves as to him being influential on the origins of the topic, which is more or less what is expressed in my less grandiose rewrite), and i don't think it is appropriate to refer to him as "on of the greatest" based on these sources. More precisely :

1. Regarding the "art review" i am referring to https://www.frieze.com/article/room-sound-objects-abstractions-art-catherine-christer-hennix. This source is entirely inappropriate here and should be removed.

2. As i said the book by Gillies does not seem to be about the history of topology and a passing remark in a book on another topic cannot be used to justify such a grandiose claim. Likewise for the SEoP (as the later has other details of interest and is freely accessible i agree it is fine here).

You are welcome to remove "greatest mathematician" from Grothendieck's page and others, i'll support it if you do that.

I don't understand your last sentence at all. jraimbau (talk) 06:09, 18 March 2024 (UTC)

P.S. Regarding the respective importance of Poincaré and Brouwer : the "Analysis situs" series is one of the most influential works on XXth century mathematics, for instance for the Poincaré conjecture but also for formally introducing homology ; he also was influential on the development of dynamical systems, and to a certain extent of special relativity. I don't think Brouwer's work in mathematics, however important for the development of formalism, cannot compare to that in terms of influence and width. jraimbau (talk) 06:15, 18 March 2024 (UTC)

I'm sorry, but this is getting more and more absurd. Precise arguments you say? I can't find one argument in your edit summary (even though that isn't the place to argue) or anywhere else, let alone a precise one! You wrote: "reformulate "founder of topology"" How is that an argument? The source, the SEoP, says something completely different, namely: "In classical mathematics, he founded modern topology by establishing, for example, the topological invariance of dimension and the fixpoint theorem." You didn't "reformulate" that, you simply changed it into something different (grandiose or not has nothing to do with it; there's a source on which this sentence is based, and you just made your own version of it; that's WP:OWN RESEARCH...).

Apart from that, similar claims can be read elsewhere, i.e. on Encyclopedia Britannica we read: "In view of his remarkable contributions, many mathematicians consider Brouwer the founder of topology." Another example in the Collected Works by Brouwer, Hans Freudenthal wrote: "Because of this discovery we may rightly claim that, notwithstanding all precursors, modern topology started with Brouwer". How many more references do you want? The same can be said about stressing Brouwer's importance. In an article on Brouwer, Van Dalen writes: "Brouwer was one of the world's leading mathematicians and logicians". A similar claim was made by James Pierpont, who talked about Brouwer as "one of the greatest living mathematicians".

May I ask how you intend to substantiate the kind of claims people make on Wikipedia? You seem to have no problem with what has been written about Hilbert, even though there isn't a single source that substantiate the claim in that article. It seems to me you have very strong opinions about these matters, but time after time you refuse to give proper sources for your opinions. Why? You criticize for instance the source of Gillies, even though he is a historian of science and a mathematician. In another article he writes as an introduction: "L.E.J. Brouwer (1881-1966) was a Dutch mathematician and philosopher of mathematics. Indeed he is generally recognised as one of the leading mathematicians and philosophers of mathematics of the twentieth century."

Also, I'm not disputing the importance of Poincaré, apart from his work in mathematics he certainly did important work in the field of physics. The influence of Brouwer in that respect lies elsewhere, namely more in the domain of philosophy and computer science. Lastly with regard to the source of that art page, I agree, that should indeed be removed. GoneWithThePuffery (talk) 14:15, 18 March 2024 (UTC)

I'm fairly sure that you can find sources about any mathematician of significant stature calling them "one of the greatest". I think it is still inappropriate to put that in the lede of a wikipedia page; it's just the kind of substance-less statement which people tend to make and which has no encyclopedic content. I'm not going to insist on that much, as i agree with you that there are unfortunately too many instances of this on articles in Wikipedia and i don't want to have to go edit them to prove to you that i'm discussing in good faith.

Regarding your other claim i stand by my earlier assertions. I believe that "he is known as the founder of modern topology" is wrong as stated: what the sources show is that certain people claim so and i doubt very much that there is a consensus about that among topologists and historians of science. To me the reformulation "He is considered as one of the founders of modern topology" reflects the existence of these sources (which do not show a consensus) better than the formulation in the version you restored. Compare with the lede on the following pages :

• Felix Hausdorff, who can also rightly can be called a founder of topology (cf. [1] : "Hausdorff established topology as an independent discipline in mathematics.").
• Henri Poincaré, who is generally regarded as having "founded" algebraic topology (cf. [2] : "Entre 1895 et 1904, Henri Poincaré a fondé la topologie algébrique").

For each of these there is a formulation similar to what i propose in the lede. It seems that my proposal would uniformise between these pages. (I don't think that being called "a" instead of "the" founder of modern topology diminishes Brouwer's accomplisments much).

We seem to agree the art review at least. jraimbau (talk) 18:23, 18 March 2024 (UTC)